We study a correlation function for the one-dimensional isotropic ${ XY}$ model (${ XX0}$ model), which is called the Emptiness Formation Probability (EFP). It is the probability of the formation of a ferromagnetic string in the anti-ferromagnetic ground state. Using the expression of the EFP as a Toeplitz determinant, we discuss its asymptotic behaviors. We also compare the analytical results with numerical calculations as the density-matrix renormalization group and the quantum Monte-Carlo method.
Categories: cond-mat.stat-mech hep-th nlin.SI